doi: 10.1685/journal.caim.534

Spectral and analytic properties of non-local Schrödinger operators and related jump processes

Jozsef Lorinczi, Kamil Kaleta, Samuel Durugo

Abstract


We discuss recent developments in the spectral theory of non-local Schrödinger operators via a Feynman-Kac-type approach. The processes we consider are subordinate Brownian motion and a class of jump Levy processes under a Kato-class potential. We discuss some explicitly soluble specific cases, and address the spatial decay properties of eigenfunctions and the number of negative eigenvalues in the general framework of the processes we introduce.

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Communications in Applied and Industrial Mathematics
ISSN: 2038-0909